A275970 a(n) = 3*2^n + n - 1.

2, 6, 13, 26, 51, 100, 197, 390, 775, 1544, 3081, 6154, 12299, 24588, 49165, 98318, 196623, 393232, 786449, 1572882, 3145747, 6291476, 12582933, 25165846, 50331671, 100663320, 201326617, 402653210, 805306395, 1610612764, 3221225501, 6442450974, 12884901919, 25769803808, 51539607585, 103079215138, 206158430243, 412316860452, 824633720869

Offset: 0

Author

Miquel Cerda, Aug 15 2016

Keywords

• nonn
• easy

Links

• Carauleanu Marc, Table of n, a(n) for n = 0..400
• S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Programs

Mathematica

LinearRecurrence[{4,-5,2},{2,6,13}, 25] (* or *) Table[3*2^n + n - 1, {n,0,25}] (* G. C. Greubel, Aug 18 2016 *)

PARI

a(n)=3*2^n+n-1 \\ Charles R Greathouse IV, Aug 27 2016

Formula

a(n) = 2*a(n-1) - n + 2.

a(n+1) - a(n) = A181565(n)

a(n) = A007283(n) + n - 1

a(n) = A083706(n) + A000079(n)

a(n) = A145071(n+1) - A000079(n)

a(n) = A079583(n) + A005408(n)

a(n) = A068156(n+1) - A079583(n)

a(n) = (A068156(n+1) + A005408(n)) / 2

a(n) = A000225(n) + A000325(n+1) + A005408(n)

a(n) = A068156(n+1) - A000225(n) - A000325(n+1)

a(n) = A068156(n+1) - A007283(n) + n + 2.

a(n) = A000079(n) + A000225(n) + A000295(n) + A005408(n)

From G. C. Greubel, Aug 18 2016: (Start)

O.g.f.: (2 - 2*x - x^2)/( (1-2*x)*(1-x)^2 ).

E.g.f.: 3*exp(2*x) + (x-1)*exp(x).

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-2). (End)